A big part of the pitch for states to participate in the Medicaid expansion through President Obama‘s health care law is rooted in the fallacy that it represents “free” money from Washington.

Republican governors who have fought conservatives to expand Medicaid in their states have relied on the argument that it would be cost-free to residents. Gov. John Kasich, R-Ohio, presented it as “a chance to bring Ohio money back to Ohio.” On her official website, Gov. Jan Brewer has a page dedicated to selling the Medicaid expansion as “The Conservative Choice for Arizona,” which boasts that the plan carries “no state expense” and comes at “no cost.”